A laser amplifies light by concentrating an external source of energy into light waves of a particular wavelength and direction so that resulting light waves are spatially and temporally aligned, or in phase. A laser medium may be a gas, a liquid, or a solid state material such as a crystal. A crystal laser medium may be doped with atoms of another material to alter the properties of the laser medium.
As is well known to those skilled in the art, basic operating principles of a laser are understood to be as follows: when a laser medium is energized, electrons within atoms comprising the laser medium are temporarily elevated to a higher atomic energy level, a process called pumping absorption. When high-energy electrons return to a lower energy state, the atom emits light at a wavelength determined by the separation between the two energy levels. This process is called stimulated or spontaneous emission, and visible light emitted during the emission process is referred to as fluorescence. To achieve amplification at a particular wavelength, the number of stimulated emission events must exceed the number of stimulated absorption events, a condition called a population inversion that requires maintaining more electrons at the upper energy level than at the lower level. This population inversion is achieved by “pumping” the laser with an external source of energy, such as an electric current or another laser beam. By containing a lasing medium in a box, or cavity, with light-reflective interior surfaces, light waves produced by stimulated emission resonate within the cavity and reinforce one another to form a coherent, collimated beam. A portion of the coherent laser beam thus produced is permitted to escape through one end of the cavity. A pulsed laser beam may be generated by periodically interrupting a continuous beam. Typical pulse repetition frequencies exceed 100,000 pulses per second, or 100 kHz.
Laser pumping efficiency is expressed by a “quantum defect” level, defined as the percentage of pumping energy lost. Excess energy resides in the laser medium as heat. The quantum defect percent is given byq=(1−ωs/ωp)·100,in which ωs is a frequency associated with the laser energy transition and ωp is the pumping light frequency. Thus, a low quantum defect is desirable. In the case of a lasing material pumped by an intense light source, excited state absorption (ESA) reduces pumping efficiency. A factor γ=[1+(δv/Δv)2]−1 is used to measure overlap between emission and absorption lines, in which δv is the frequency difference between the emitting transition and the absorbing transition, and Δv is the full line-width at half intensity of the pumping diode spectrum. A small value of γ corresponds to a low probability of an ESA transition and a high efficiency pumping scheme with respect to ESA.
High-power, diode-pumped solid state (DPSS) pulsed lasers, with power levels on the order of tens of Watts, are preferred for applications such as micromachining, via drilling of integrated circuits, and ultraviolet (UV) conversion. Neodymium:Yttrium Vanadate (Nd:YVO4) and Neodymium:Gadolinium Vanadate Nd:GdVO4 lasers, made with Nd3+-doped Vanadium Oxide (VO4) crystals are good candidates for high power applications because they feature a high energy absorption coefficient over a wide bandwidth of pumping wavelengths. However, vanadate has poor thermo-mechanical properties, compared with other crystal candidates (e.g., Neodymium:Yttrium Aluminum Garnet, or Nd:YAG) in that the material is stiff and fractures easily when thermally stressed. Vanadate fractures under 53 MPa of pressure, while Nd:YAG crystals used in conventional lasers can withstand pressures as high as 138 MPa. Thus, Nd:YAG allows for a correspondingly larger maximum pump power than does vanadate.
In general, power absorbed by a lasing medium decreases exponentially from the point of entry, according to P=Po(1−e−αL), where Po is applied pump power, α is the absorption coefficient, and L is the length of the crystal rod. If pump power is absorbed preferentially along one axis of a crystal lattice, the absorption coefficient in the direction of that axis is larger. The high power pumping produces a high temperature gradient and associated tensile stress, which may cause asymmetric “thermal lensing” effects or crystal fracture, especially serious for asymmetric absorptions. A symmetric absorption coefficient indicates that pump energy is absorbed equally in all directions, which can expend the heat along the gain medium and in turn reduce excessive thermal stress in the crystal. The inherent structure of the Nd:YVO4 crystal unit cell, having a dimension along the optic axis c=6.2 Å that differs from equivalent dimensions perpendicular to the optic axis, a=b=7.1 Å, results in asymmetric absorption.
Thermal lensing relates to a generally undesirable phenomenon in high power solid state lasers in which heat from excess energy absorption raises the material temperature and distorts the index of refraction of the laser crystal. This distortion results in an effective “lens,” in which the focal length varies inversely with absorbed pump power. Excessive thermal lensing is detrimental to solid state laser performance because of beam distortion and reduced laser conversion efficiency. Proper control of thermal lensing in the lasing material (e.g., by lowering the quantum defect level) is therefore a critical factor in high power laser engineering.
Complications such as thermal lensing have thus far limited the power output of vanadate DPSS lasers in TEM00 mode to less than 30 W. Limitations caused by thermal lensing and thermal fracture are described in Peng, Xiaoyuan; Xu, Lei; and Asundi, Anand; Power Scaling of Diode-Pumped Nd:YVO4 Lasers, IEEE Journal of Quantum Electronics, Vol. 38, No. 9, 1291-99, September 2002.
Factors influencing inhomogeneous absorption, thermal lensing, and fluorescence lifetimes include doping concentration and physical dimensions of the laser crystal, as well as pumping wavelength and polarization. A typical pumping wavelength used with vanadate crystals is 808 nm, and typical doping concentrations are 0.2% at.-0.5% at, while values below 0.1% at. are difficult to achieve with the degree of control afforded by current manufacturing processes. Typical crystal rod lengths range from 7 mm-15 mm.
Vanadate crystal is an anisotropic material, in which the pump energy absorption, and therefore the laser gain, is polarization-dependent, absorbing some polarized waves more readily than others. A change in the polarization state of the pump laser beam, in response to temperature fluctuations (thermal effects), or random shifts in the polarization direction, may therefore contribute further to inhomogeneous absorption. It may be advantageous to force the pump laser beam to be either polarized in a certain direction or de-polarized to control this effect.
A 40% reduction in thermal lensing effects is reported by Dudley et al., (CLEO 2002 Proceedings) by pumping at 880 nm directly into the upper energy level of the laser transition, rather than at the traditional 808 nm wavelength. This reduction in thermal lensing effects is thought to result from a decrease in the quantum defect level from 24% to 17%, rather than from improved absorption symmetry, because the directional components of the absorption coefficient still differ by a factor of three. However, the absorption bandwidth that a pump delivers at 880 nm is only 2.5 nm compared to commercial products that offer a 4 nm bandwidth.
McDonagh et al., Optics Letters, Vol. 31, No. 22, Nov. 15, 2006 published results for a high-power Nd:YVO4 laser with 0.5% at. Nd3+ doping, pumped at 888 nm. With reference to FIG. 1, lasing wavelengths for Nd:YVO4 normally include 914.5 nm, 1064 nm, and 1342 nm. As published by A. Schlatter, et al., Optics Letters, Vol. 30, No. 1, Jan. 1, 2005, when operating Nd:YVO4 for emission at 914.5 nm, a neodymium ion behaves as a quasi-three-level system. The low laser energy level Z5 is only 433 cm−1 above the ground state, a condition that results in a high lower-state population of 5% at room temperature. Therefore, Schlatter concludes that there is difficulty in achieving Nd:YVO4 lasing at 914.5 nm because a very bright pumping light source is needed to overcome the high threshold caused by a high population in the state of 433 cm−1.
FIGS. 2, 3, 4, and 5 illustrate certain limitations of vanadate crystals. A primary limitation is maximum pump power, which is the amount of pump energy that may be delivered to a crystal before it fractures. FIG. 2 is a plot comparing calculated maximum pump power levels 100 and measured maximum pump power levels 102 for a doped vanadate crystal, 3 mm×3 mm×5 mm, with a pump beam radius of 0.4 mm. Dependence of fracture-limited pump power on crystal properties is well established. In this case, crystal dimensions, pump beam radius, pump wavelength, and laser-active ion doping concentration determine the power operating range of the laser device. FIG. 2 compares calculated results with three experimental data points 104, indicating the pump power at which vanadate crystals actually fractured for various doping concentrations. The calculation used to predict the curve shown in FIG. 2 is a three-dimensional finite element model that simulates thermal effects of pumping a doped crystal by solving Fourier's heat conduction equation. FIG. 2 shows that low doping concentrations are desirable to prevent fracture, with 0.3% at. doping concentration 106 being optimal, allowing a maximum pump power of 37 W. FIG. 3 shows that, for an applied pump power of 30 W, just under the maximum from FIG. 2, the predicted output power 108 achieved by pumping a vanadate laser with a 0.5% doping concentration is optimized at 9 W. Results in FIGS. 2 and 3 were obtained using a diode laser pump at the conventional pumping wavelength of 808 nm.
FIGS. 4 and 5 show spatial distributions of pump power along the length of a 15 mm vanadate crystal rod that serves as a lasing gain medium. Solid curve 110 and dotted curve 112 trace, at various points along the length of the rod (a-cut), respectively, average power absorbed for polarization in the a-axis direction and average power absorbed for polarization in the c-axis of the crystal rod. An ideal crystal rod exhibits symmetric power absorption, in which both the solid and dotted curves are flat lines that coincide along the full length of the rod. The vanadate crystal rod has asymmetric power absorption with, on average, more power absorbed for polarization in the c-axis direction. Furthermore, when pump power is applied to the ends of a lasing gain medium, more power is absorbed close to the ends, while less power reaches the center, a condition referred to as “end-bulging” 120. This applies to both c- and a-axes; however, more extreme end-bulging 122 occurs in the c-direction. A reduction in end-bulging 124 and a reduction in asymmetry 126 both occur when the doping level increases from 0.3% at. (FIG. 5) to 0.5% at. (FIG. 4). The integrated temperature gradient on the cross section of the lasing crystal is greater in the c-axis direction than in the a-axis direction.